The three names now most likely to fall to the Knicks at 17 include one point guard in Georgia Tech’s Iman Shumpert, one shooting guard in Colorado’s Alec Burks and one center in USC’s 6-foot-11 Nikola Vucevic. All three are “need” positions entering tomorrow’s NBA Draft.

The least likely to fall is Burks, the 6-foot-5 sophomore shooting guard from Colorado who’s more slasher than shooter. The Knicks likely would lean toward Burks, slated as high as No. 10 to Milwaukee. Most mock drafts have him going before 17, but recent rumors have him slipping.

The Knicks are growing less optimistic point guard Jimmer Fredette, shooting guard Klay Thompson or forward Chris Singleton will slip to 17, and prospects of trading up are slim. The Knicks are more likely to try to snare a veteran and trade back in the draft, a source said.

Shumpert, meanwhile, has gotten great support in the Knicks’ board room in recent days, rising up the point-guard chart due to his workout two weeks. The 6-foot-5 Shumpert is now considered ahead of Michigan’s Darius Morris and Kansas’ Josh Selby because of his defensive ability and shooting from the perimeter.

The Knicks are fearful of point guard Chauncey Billups’ health at age 35 and Toney Douglas’ ability to play point guard full-time coming off shoulder surgery. However, there are a number of point guards they can snare later in the draft as Donnie Walsh looks to buy at least one more late first-rounder or second-rounder. Shooting guard is also a concern after rookie Landry Fields’ late-season collapse.

“He’s proved to be a really good defender on film this year in the ACC,” ESPN draft savant Fran Fraschilla said of Shumpert. “Long arms, good size. I think if he’s going to get on an NBA court early in his career, it’s going to be as much on the defensive end.”

The Post has learned if the Knicks do buy another second-round pick, the staff will consider UTEP point guard Jylyan Stone if they do not select Shumpert at 17. Stone is a burly defender and a good playmaker.

Vucevic was not considered a good value at 17 until the Chicago pre-draft camp, when he measured in at 6-foot-11¾. He is a solid, safe pick for Walsh, who has often spoken about needing to add size to Knicks following the deal for Carmelo Anthony. Yesterday, the draft site Draftexpress.com moved Vucevic up to 16 to the Sixers, ahead of the Knicks.

Fredette said yesterday on the Dan Patrick Show the Knicks and Utah are his top two choices, with the Knicks being “1A.” Fredette, of upstate Glens Falls, rooted for the Knicks as a kid. The Glens Falls Civic Center is staging a “Jamming with Jimmer” party at the arena tomorrow night.

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Spero Dedes is leaving the Lakers’ radio booth to join the Knicks to do some radio and TV. The club has not announced the move.